Question

Two horizontal forces act on a 55 kg object. One force has magnitude 65N directed 59 degrees clockwise from the positive x axis, and the other has a magnitude 35 N at 32 degrees clockwise from the positive y axis. What is the magnitude of this object's acceleration?

Answer 1

Refer below figure,

F2 θ2 01 F1

F1= 65N , θ1= 5N , F2 = 35 N , θ2= 32 N

Fnetx = F1x + F2x = F1cosθ1+F2sinθ2 = 65cos(-59) + 35sin32 = 52 N

Fnety = F1y + F2y = F1sinθ1+F2sinθ2 = 65sin(-59) + 35cos32 = -26 N

Fnet = sqrt(Fnetx^2 + Fnety^2) = sqrt(52^2 + 26^2) = 58 N

anet = Fnet/m = 58/55 = 1.05 m/s^2